Abstract
The existence of families of periodic, repeat ground track orbits in full geopotentials is demonstrated. The basic families are made of almost circular orbits except in the vicinity of the critical inclination (63.4/116.6 deg), where the eccentricity of the repeat orbits grows for almost fixed inclination. Computation of specific repeat ground track orbits for mission design can be automated providing the nominal solution in a fast, straightforward way. We illustrate this with the computation of the TOPEX nominal orbit in a 140 × 140 truncation of the GRACE Gravity Model.
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References
LARA, M. “Searching for Repeating Ground Track Orbits: A Systematic Approach,” The Journal of the Astronautical Sciences, Vol. 47, 1999, pp. 177–188.
LARA, M. “Repeat Ground Track Orbits of the Earth Tesseral Problem as Bifurcations of the Equatorial Family of Periodic Orbits,” Celestial Mechanics and Dynamical Astronomy, Vol. 86, No. 2, 2003, pp. 143–162.
LARA, M. and RUSSELL, R. P. “On the Computation of a Science Orbit About Europa,” Journal of Guidance, Control, and Dynamics, Vol. 30, No. 1, 2007, pp. 259–263.
RUSSELL, R. P. and LARA, M. “Long Lifetime Lunar Repeat Ground Track Orbits,” Journal of Guidance, Control, and Dynamics, Vol. 30, No. 4, 2007, pp. 982–993.
SEIDELMANN, P. K., ARCHINAL, B. A., AHEARN, M. F., CONRAD, A., CONSOLMAGNO, G. J., HESTROFFER, D., HILTON, J. L., KRASINSKY, G. A., NEUMANN, G., OBERST, J., STOOKE, P., TEDESCO, E. F., THOLEN, D. J., THOMAS, P. C., and WILLIAMS, I. P. “Report of the IAU/IAG Working Group on Cartographic Coordinates and Rotational Elements: 2006,” Celestial Mechanics and Dynamical Astronomy, Vol. 98, No. 3, 2007, DOI 10.1007/s10569-007-9072-y, pp. 155–180.
IRIGOYEN, M. and SIMÓ, C. “Non Integrability of the Problem,” Celestial Mechanics and Dynamical Astronomy, Vol. 55, No. 3, 1993, pp. 281–287.
DEPRIT, A. and Henrard, J. “Construction of Orbits Asymptotic to a Periodic Orbit,” The Astronomical Journal, Vol. 72, No. 2, 1969, pp. 308–316.
TAPLEY, B., RIES, J., BETTADPUR, S., CHAMBERS, D., CHENG, M., CONDI, F., GUNTER, B., KANG, Z., NAGEL, P., PASTOR, R., PEKKER, T., POOLE, S., and WANG, F. “GGM02-An Improved Earth Gravity Field Model from GRACE,” Journal of Geodesy, Vol. 79, 2005, DOI 10.1007/s00190-005-0480-z, pp. 467–478.
LARA, M. and PELÁEZ, J. “On the Numerical Continuation of Periodic Orbits: An Intrinsic, 3-Dimensional, Differential, Predictor-Corrector Algorithm,” Astronomy and Astrophysics, Vol. 389, Feb. 2002, pp. 692–701.
HENÒN, M. “Exploration Numérique du Problème Restreint. II.—Masses égales, stabilité des orbites périodiques,” Annales d’Astrophysique, Vol. 28, No. 2, 1965, pp. 992–1007.
VALLADO, D.A. Fundamentals of Astrodynamics and Applications, 2nd edition, 2004, Space Technology Library, Microcosm Press & Kluwer Academic Publishers, pp. 792 ff.
LARA, M. Sadsam: a Software Assistant for Designing Satellite Missions, Report CNES num. DTS/MPI/MS/MN/99-053, 1999, 75 pages.
FRAUENHOLZ, R. B., BHAT, R. S., and SHAPIRO, B. E. “Analysis of the TOPEX/Poseidon Operational Orbit: Observed Variations and Why,” Journal of Spacecraft and Rockets, Vol. 35, No. 2, 1998, pp. 212–224.
BROUCKE, R. “Stability of Periodic Orbits in the Elliptic, Restricted Three-Body Problem,” AIAA Journal, Vol. 7, 1969, pp. 1003–1009.
LARA, M. and SAN JUAN, J. F. “Dynamic Behavior of an Orbiter Around Europa,” Journal of Guidance, Control and Dynamics, Vol. 28, No. 2, 2005, pp. 291–297.
BROUCKE, R. “Numerical Integration of Periodic Orbits in the Main Problem of Artificial Satellite Theory,” Celestial Mechanics and Dynamical Astronomy, Vol. 58, No. 2, 1994, pp. 99–123.
BROUCKE, R. “Periodic Collision Orbits in the Elliptic Restricted Three-Body Problem,” Celestial Mechanics and Dynamical Astronomy, Vol. 3, 1971, pp. 461–477.
COFFEY, S., DEPRIT, A., and DEPRIT, E. “Frozen Orbits for Satellites Close to an Earth-Like Planet,” Celestial Mechanics and Dynamical Astronomy, Vol. 59, No. 1, 1994, pp. 37–72.
PINES, S. “Uniform Representation of the Gravitational Potential and its Derivatives,” AIAA Journal, Vol. 11, Nov. 1973, pp. 1508–1511.
LUNDBERG, J. B. and SCHUTZ, B. E. “Recursion Formulas of Legendre Functions for use with Nonsingular Geopotential Models,” Journal of Guidance, Vol. 11, No. 1, 1988, pp. 31–38.
HAIRER, E., NØRSETT, S. P., and WANNER, G. Solving Ordinary Differential Equations. Nonstiff Problems, 2nd edition, 1993, Springer Series in Computational Mathematics, Vol. 8, pp. 181–185.
BOND, V. “Error Propagation in the Numerical Solution of the Differential Equations of Orbital Mechanics,” Celestial Mechanics, Vol. 27, No. 1, 1982, pp. 65–77.
LAWSON, C. L. and HANSON, R. J. Solving Ordinary Least Squares Problems, 1974, Prentice-Hall.
Math77 Reference Manual, edited by Lisa K. Jones and Laurie Seaton, Language Systems Corporation, Sterling, Va., 1994.
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Lara, M., Russell, R.P. Fast design of repeat ground track orbits in high-fidelity geopotentials. J of Astronaut Sci 56, 311–324 (2008). https://doi.org/10.1007/BF03256555
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DOI: https://doi.org/10.1007/BF03256555